A hybrid ensemble Kalman filter approach to data assimilation in a two-dimensional shallow water model

Our hybrid ensemble Kalman filter, previously tested in a Lorenz system, is now explored using a two-dimensional shallow water model. The hybrid ensemble Kalman filter effectively combines the ensemble Kalman filter (EnKF) and nudging to achieve more gradual data assimilation by computing the nudging coefficients from the flow-dependent, time-varying error covariances of the EnKF. This hybrid EnKF can also transform the gain matrix of the EnKF into additional terms in the model's predictive equations to assist in the data assimilation process.

The hybrid EnKF approach is tested under different initial conditions and observation scenarios. It has been shown to contribute to more rapid assimilation of the data and better fit of an analysis to the data compared to both the nudging and EnKF. It allows the gain matrix of the EnKF to be applied gradually in time, reducing the error spikes between assimilation times common with intermittent data assimilation. Although the hybrid EnKF is comparable in cost to the EnKF, its more gradual assimilation of the data in time promotes better intervariable consistency and retention of observation information than the EnKF. These shallow-water model applications, along with our previous work using the Lorenz system, will be used to design and implement such a hybrid data assimilation approach in the WRF-ARW.